2.1 Contrail formation process

Water vapour and particles in aero engine exhaust can give rise to contrails in the wake of aircrafts and are essentially formed of ice crystals. The evolution of aircraft wakes can be categorised into four regimes [Reference Paoli and Shariff8]: Jet, Vortex, Dissipation and Diffusion regimes, while the formation process of ice crystals can be divided into four stages [Reference Kärcher4].

In the jet regime, ice crystal formation is known to occur in two stages. A pair of vortices are induced by the aircraft wingtips, trapping most of the engine exhaust, referred to as the ‘primary wake’. During the turbulent mixing process of engine exhaust and the ambient air, ambient aerosol particles and particulate matter are also entrained in engine plumes, along with soot particles and ultrafine aqueous particles formed in the exhaust. Due to cooling effect of the mixing process, the water vapour becomes supersaturated with respect to liquid water, forming water droplets on the particles and depending on the ambient temperature could freeze thus forming ice particles.

The ice crystals then continue to develop through two further formation stages in the vortex regime. During the vortex regime, due to the mutually induced downward velocity, the vortex pair are known to descend to a lower altitude (several hundred metres). The vortex pair then induces a secondary wake, which moves upward and carries with it a part of the exhaust and ice crystals. At the beginning of the vortex regime, ice crystals formed in the jet regime perform fast growth by absorbing more ice-supersaturated water vapour from the atmosphere, presenting a visible contrail. With the downward movement of the vortex pair, ice crystals sublimate at the lower wake due to a higher temperature. Ice crystals at the upper wake continue to grow by absorbing ice-supersaturated water vapour from the entrained ambient air.

A few minutes later, the wake does not retain its structure and enters the dissipation regime, resulting in the break-up of the vortices and mixing of the wake flow with the ambient air. Ice crystals at lower altitudes sublimate due to warmer temperatures, while those entrapped in the secondary wake region last for significantly longer periods due to lower ambient temperature at higher altitudes.

The diffusion regime normally occurs within a few hours. The contrails could spread vertically and horizontally, forming contrail cirrus, and covering large areas. These processes are known to be strongly affected by wind shear, atmospheric turbulence, particulate sedimentation, and radiative processes.

2.2 Contrail formation criteria

The formation process of contrails can be indicated on the water phase diagram. For temperatures over 273.15K, the water phase diagram is shown in Fig. 1.

Figure 1. Water phase diagram (above 273.15K).

The horizontal and vertical axes are the temperature and partial pressure of the water vapour, respectively. The blue curve stands for the water vapour saturation pressure over liquid water. In the region above the liquid water saturation curve, the water vapour partial pressure is higher than the corresponding water vapour saturation pressure (supersaturated), leading to water vapour condensation. Below the curve, the water vapour is considered to subsaturated, which means water remains in the gaseous phase. As can be seen in Fig. 1, at constant water vapour partial pressure condition, the water would be converted to liquid form at a certain temperature. This point of phase change for that condition is demarcated by the liquid water saturation curve. Similarly, if water were to exist in liquid form at a constant partial vapour pressure, any increase in temperature over that specified by the liquid water saturation curve would result in the water converted to vapour form.

The water vapour saturation pressure is a function of static temperature. When the temperature is below 273.15K, there are three phases of water on the diagram, as shown in Fig. 2.

Figure 2. Water phase diagram (below 273.15K).

The blue curve stands for the water vapour saturation pressure with respect to liquid water, while the orange curve represents the water vapour saturation pressure with respect to ice. For gaseous water with constant partial pressure, with the reduction of temperature, the vapour firstly condenses into solid phase and then becomes liquid water.

For contrails, as shown in Fig. 3, point A represents the ambient water vapour condition, point B represents the water vapour condition at the engine exit. The engine exhaust is not uniform, consisting of the hot and moist core gas and relatively cold and dry bypass air; therefore, point B is the condition that the core gas and bypass air are assumed to mix homogeneously.

Figure 3. Non-persistent contrail formation process.

The line from B to A represents a hypothetical line representing the cooling and dilution process of the engine plume achieved through mixing with cooler (and drier) ambient air. This process is assumed to be adiabatic and vapour conserving; the vapour and heat are assumed to diffuse at the same rate. Therefore, the mixing line BA is represented as a straight line on the water phase diagram. From B to A, the mixing line first crosses the ice saturation curve at point 1 and then crosses the liquid water saturation curve at point 2. Before point 1, the water vapour in the plume is subsaturated. Between points 1 and 2, the water vapour becomes ice-supersaturated, but ice crystals do not form due to the lack of nucleation process. After point 2, the water vapour is liquid-water-supersaturated, condensing on the nucleation agents in the plume and forming water droplets. With the further mixing of engine plume and ambient air, the mixing line crosses the liquid water saturation curve again at point 3. After point 3, the water droplets start to freeze because of the ice-supersaturated condition; ice crystals form at this stage.

Finally, the mixing line ends at the ambient condition point. In Fig. 3, the ambient condition is subsaturated, so ice crystals sublimate soon, resulting in non-persistent contrails.

If point A is between the liquid water saturation curve and ice saturation curve, as shown in Fig. 4, the ambient condition is ice supersaturated. In an ice-supersaturated region, once contrails form, ice crystals can last for a long time, leading to persistent contrails.

Figure 4. Persistent contrail formation process.

In the three cases in Fig. 5, contrails do not form. In (a) and (b), the mixing line crosses the ice saturation curve at point 1; the water vapour becomes ice supersaturated. However, without the emergence of water droplets, ice crystals cannot form; therefore, no contrail can form no matter the ambient condition is subsaturated (case (a)) or ice-supersaturated (case (b)). In case (c), the whole mixing process is subsaturated, so contrails cannot form.

Figure 5. No contrail formation.

In brief, on the water phase diagram, if the mixing line crosses the liquid water saturation curve, contrails form. Once contrails form, if the ambient condition is supersaturated, contrails are persistent; if the ambient condition is subsaturated, contrails are non-persistent.

2.3 Contrail prediction model: Schmidt-Appleman criterion

Based on Section 2.2, a contrail prediction model is summarised, called the Schmidt-Appleman criterion. The slope of the mixing line can be calculated if the engine performance data and the ambient conditions are known. Once the slope of the mixing line is confirmed, a threshold temperature can be defined; if the ambient temperature is lower than the threshold temperature, contrails form; otherwise, contrails do not form.

Point B stands for the water vapour condition at the engine exhaust and point A stands for the ambient water vapour condition. The mixing line BA is straight, so its slope can be defined as [Reference Schumann9, Reference Gierens10]:

(1) \begin{align}G = \frac{{{c_P} \cdot E{I_{{H_2}O}} \cdot p}}{{\varepsilon \!\left( {1 - \eta } \right)\!Q}}\end{align}

Where:

• • $p$ is the air pressure

• • $\varepsilon $ is the ratio of molar masses of water and air

• • $Q$ is the lower heat value (LHV) of the fuel (amount of heat produced by burning a kg of fuel)

• • $\eta $ is the engine overall efficiency

• • ${c_P}$ is the specific heat capacity of air

• • ${\rm{E}}{{\rm{I}}_{{{\rm{H}}_2}{\rm{O}}}}$ is the water emission index of the fuel (for kerosene, the ${\rm{E}}{{\rm{I}}_{{{\rm{H}}_2}{\rm{O}}}}$ is 1.26, which means the combustion of 1kg of kerosene produces 1.26kg of water)

Therefore, once the engine performance data ( $\eta, {\rm{\;}}E{I_{{H_2}O}},{\rm{\;}}Q$ ) and ambient conditions ( $p,{\rm{\;}}{c_P}$ ) are obtained, with the known constants ( $\varepsilon $ ), the slope of the mixing line can be calculated. The ambient condition and the mixing line slope can confirm the position of the mixing line on the water phase diagram. Equation (1) shows the parameters that affect the mixing line slope. For a specific engine at a specific cruise altitude, the ambient pressure $p$ , the specific heat capacity of air ${c_P}$ and molar masses of water and air $\varepsilon $ cannot be changed. For current engines using kerosene as the fuel, the fuel heat value $Q$ cannot be changed. Therefore, only a reduction in ${\rm{E}}{{\rm{I}}_{{{\rm{H}}_2}{\rm{O}}}}$ or $\eta $ can lower the $G$ , while reducing $\eta $ will lead to a significant increase in specific fuel consumption (SFC), reducing ${\rm{E}}{{\rm{I}}_{{{\rm{H}}_2}{\rm{O}}}}$ is the emphasis in the following study.

${\rm{E}}{{\rm{I}}_{{{\rm{H}}_2}{\rm{O}}}}$ is the water emission index of the fuel; from a contrail mitigation perspective, the ${\rm{E}}{{\rm{I}}_{{{\rm{H}}_2}{\rm{O}}}}$ can represent the water content in the exhaust gas at the exhaust nozzle exit plane. Therefore, by removing water content from the exhaust gas before discharging, ${\rm{E}}{{\rm{I}}_{{{\rm{H}}_2}{\rm{O}}}}$ can be reduced. By applying the Schmidt-Appleman criterion, required water removal for contrail mitigation at different ambient relative humidity (RH) can be calculated for a specific engine. A threshold condition can be defined when the mixing line touches the liquid water saturation curve at the tangential point, which is named the liquid maximum (LM) point (Fig. 6). The LM point can be confirmed by the following equations [Reference Schumann9]:

(2) \begin{align}\frac{{d{e_{sat,l}}\left( {{T_{LM}}} \right)}}{{d{T_{LM}}}} = G\end{align}

(3) \begin{align}{e_{LM}} = {e_{sat,l}}\left( {{T_{LM}}} \right)\end{align}

For a specific $G$ , the corresponding threshold mixing line can be confirmed on the water phase diagram if LM is obtained. As indicated in Fig. 7, If the actual mixing line (the solid line) is at the left side of the threshold mixing line (the dotted line), the actual mixing line must cross the liquid water saturation curve, which means contrails form; if the actual mixing line (the dashed line) is at the right side, contrails do not form.

The threshold ambient condition point liquid critical (LC) is defined on the threshold mixing line, between the LM point and the horizontal axis; its position is determined by the ambient RH [Reference Schumann9]:

(4) \begin{align}{T_{LC}} = {T_{LM}} - {{{e_{sat,l}}\left( {{T_{LM}}} \right) - RH \cdot {e_{sat,l}}\left( {{T_{LC}}} \right)} \over G}\end{align}

(5) \begin{align}{e_{LC}} = RH \cdot {e_{sat,l}}\left( {{T_{LC}}} \right)\end{align}

Figure 6. The threshold condition.

Figure 7. Using threshold condition to predict contrail formation.

As shown in Fig. 8, for example, when the ambient RH is 50%, the LC point is the crossing point of the threshold mixing line and the 50% RH curve (the grey curve, $e = 50{\rm{\% }} \cdot {e_{sat,l}}\left( T \right)$ ). The liquid water saturation curve is the 100% RH curve; thus, the LM point is the LC point when the ambient RH is 100%. The threshold mixing line, the liquid water saturation curve and the horizontal axis form a contrail zone, shown in Fig. 8 as a light blue zone. If the ambient condition point falls in the contrail zone, the actual mixing line must be at the left side of the threshold mixing line, crossing the liquid water saturation curve, which means contrail formation. If the ambient temperature is lower than the ${T_{LC}}$ , the ambient point is in the contrail zone; otherwise, it is out of the contrail zone, which means no contrail formation.

Figure 8. The threshold ambient condition.

In brief, the contrail prediction model is simplified as a comparison between the ambient temperature and corresponding RH-based threshold temperatures. If ${T_a}{\rm{\;}} \gt {T_{LC}}{\rm{\;}}$ , contrails do not form; if ${T_a} \lt {T_{LC}}$ , contrails form.

Figure 9 shows two different mixing lines. The solid line has a higher slope, forming a larger contrail area (dark blue area + light blue area), covering the ambient condition point, so contrails form. The dashed line has a lower slope and a smaller contrail area (light blue area), which cannot cover the ambient condition point, and contrails will not form. Therefore, a lower mixing line slope tends to reduce the possibility of contrail formation.

Figure 9. Mixing line slope’s impact on contrail formation.

4.1 The water removal characteristic plot

The water removal characteristic plot for the baseline kerosene fuelled LEAP 1-A engine is shown in Fig. 16. Every point on the plot refers to a combination of water removal percentage and the local ambient RH. If the point falls in the dark blue area, which represents higher levels of water removal percentage, contrail will not form. If the point falls in the contrail area, which refers to the light blue area and yellow area, contrail will form. The plot can indicate the lowest water removal percentage required for the purpose of contrail mitigation.

The nine cases of Table 1 can be located on the plot. On the plot, it can be easily observed that with the increase of ambient RH, the lowest water removal percentage for contrail avoidance also increases. When the ambient RH is 0, the minimum water removal for contrail avoidance is 36%; for ambient RH = 100%, the requirement is at least 76%. However, as discussed in Section 1, only persistent contrails and cirrus contribute to the RF, so the water removal strategies only apply to conditions that enable the formation of persistent contrails, which have ambient RHs over 60%. Therefore, according to the plot, around 52–76% of water removal is required for contrail mitigation for the baseline LEAP engine depending on the ambient RH.

4.2 The water removal characteristic plot for hydrogen fuelled engine

The utilisation of hydrogen as an aviation fuel has gained much attention in recent years. As a sustainable fuel, hydrogen has considerable potential to reduce the aviation environmental footprint. By using hydrogen as the fuel, aircraft can achieve zero-carbon and low ${\rm{N}}{{\rm{O}}_{\rm{x}}}$ emissions.

Figure 16. Water removal characteristic plot for kerosene fuelled LEAP engine.

The water emission index of hydrogen is 9, which means the combustion of 1kg of hydrogen produces 9kg of water, while it is 1.26 for kerosene. Assuming the same combustion heat release, the water produced by the combustion of hydrogen is about 2.6 times the water produced by burning kerosene. The significant increase in water vapour emission increases the possibility of contrail formation as the mixing line slope on the water phase diagram is higher. The water removal characteristic plots of kerosene and hydrogen fuelled aircraft show significant differences. The water removal characteristic plot for hydrogen fuelled LEAP engine is shown in Fig. 17. The hydrogen fuelled engine model is designed to produce the same net thrust as the kerosene fuelled engine model.

Figure 17. Water removal characteristic plot for hydrogen fuelled LEAP engine.

Compared to the kerosene fuelled engine, the hydrogen fuelled engine presents a higher water removal requirement for contrail mitigation. Depending on the ambient RH, 82–91% water removal is required.

4.3 Water removal through vapour condensation

In previous sections, the fuel heat value used in the Schmidt-Appleman criterion is the LHV of the fuel, which means the heat released by burning per kg of the fuel if the water produced by the combustion process is finally in gaseous state. To extract water vapour from the engine exhaust, the most widely considered approach is to let the vapour condense, so the liquid water can be separated from the gaseous flow. The condensation process of water vapour releases latent heat, and this amount of heat is added to the aircraft plume so the utilisation of LHV in the Schmidt-Appleman criterion is no longer accurate as not all water is discharged in gaseous state. When the water product is finally in the liquid state, the heat released by burning per kg of the fuel is the higher heat value (HHV). If the percentage of water extraction is λ, finally λ of the water will be in liquid state while (1-λ) of water will be in gaseous state; therefore, λ of the fuel burned releases the HHV and (1-λ) of the fuel burned releases the LHV. Then the fuel equivalent heat value (EHV) can be defined based on the percentage of water extraction to include the latent heat released by water condensation into consideration:

(6) \begin{align}EHV = \lambda HHV + \left( {1 - \lambda } \right)LHV\end{align}

The slope of the mixing line then becomes:

(7) \begin{align}G = {{{c_P} \cdot E{I_{{H_2}O}} \cdot p} \over {\varepsilon \!\left( {1 - \eta } \right)\!EHV}}\end{align}

By using the EHV, the water removal characteristic plot for the kerosene fuelled LEAP engine is shown in Fig. 18.

Figure 18. Water removal characteristic plot considering the latent heat.

The minimum required water removal percentage considering the latent heat is 51–75% depending on the ambient RH, slightly lower than the requirement in Section 4.1, which is 52–76%. The latent heat makes the EHV higher than the LHV, so the mixing line slope can be lower, which reduces the possibility of contrail formation, and hence a lower water removal requirement. Using the EHV instead of LHV, the calculation results are more accurate as the latent heat released by water vapour condensation is also considered.

4.4 Water discharging system

The design point fuel mass flow rate of the kerosene fuelled engine model is 1.074kg/s and the water emission index of kerosene is 1.26; therefore, at design point, the water mass flow rate in the exhaust flow is 1.353kg/s. According to the discussion in Section 4.1, around 52–76% of water removal is required for contrail mitigation; therefore, around 0.704–1.028kg/s of water is expected to be extracted. Similarly, for the hydrogen fuelled engine model, 3.014–3.345kg/s of water is expected to be extracted.

The water extracted from the exhaust flow is expected to be discharged immediately to the environment, because the extra weight due to water storage onboard leads to fuel burn penalty. However, emitting liquid water may not be a good choice as the turbulence may break large water droplets into small water droplets, and the small water droplets will freeze and form contrails.

A possible choice of the water discharging system is to emit the water in the form of large ice crystals, as shown in Fig. 19. The extracted water is transferred to a freezing system by a pump. In the freezing system, the water freezes and forms large ice crystals. Once the large ice crystals are emitted, they will not stay at high altitude but sediment soon, so contrail formation can be prevented.

Figure 19. Water discharging system.